arXiv subjects

R. Chandrashekar

Publications and source records attributed to R. Chandrashekar.

9 recordsLinked to original sources

arXiv2022

Inverse Laplace transform based on Widder's method for Tsallis exponential

A generalization of the Laplace transform based on the generalized Tsallis $q$-exponential is given in the present work for a new type of kernel. We also define the inverse transform for this generalized transform based on the complex integration method. We prove identities corresponding to the Laplace transform and inverse transform like the $q$-convolution theorem, the action of generalized derivative and generalized integration on the Laplace transform. We then derive a $q$-generalization of the inverse Laplace transform based on the Post-Widder's method which bypasses the necessity for a complex contour integration. We demonstrate the usefulness of this in computing the Laplace and inverse Laplace transform of some elementary functions. Finally we use the Post-Widder's method based inverse Laplace transform to compute the density of states from the partition function for the case of a generalized classical ideal gas and linear harmonic oscillator in $D$-dimensions.

math-ph↗

arXiv2022

Quantum coherence dynamics of displaced squeezed thermal state in a Non-Markovian environment

The dynamical behavior of quantum coherence of a displaced squeezed thermal state in contact with an external bath is discussed in the present work. We use a Fano-Anderson type of Hamiltonian to model the environment and solve the quantum Langevin equation. From the solution of the quantum Langevin equation we obtain the Green's functions which are used to calculate the expectation value of the quadrature operators which are in turn used to construct the covariance matrix. We use a relative entropy based measure to calculate the quantum coherence of the mode. The single mode squeezed thermal state is studied in the Ohmic, sub-Ohmic and the super-Ohmic limits for different values of the mean photon number. In all these limits, we find that when the coupling between the system and the environment is weak, the coherence decays monotonically and exhibit a Markovian nature. When the system and the environment are strongly coupled, we observe that the evolution is initially Markovian and after some time it becomes non-Markovian. The non-Markovian effect is due to the environmental back action on the system. Finally, we also present the steady state dynamics of the coherence in the long time limit in both low and high temperature regime. We find that the qualitative behavior remains the same in both the low and high temperature limits. But quantitative values differ because the coherence in the system is lower due to thermal decoherence.

quant-ph↗

arXiv2016

Distribution of quantum coherence in multipartite systems

The distribution of coherence in multipartite systems in examined. We use a new coherence measure with entropic nature and metric properties, based on the quantum Jensen-Shannon divergence. The metric property allows for the coherence to be decomposed into various contributions, which arise from local and intrinsic coherences. We find that there are trade-off relations between the various contributions of coherence, as a function of parameters of the quantum state. In bipartite systems the coherence resides on individual sites or distributed among the sites, which contribute in a complementary way. In more complex systems, the characteristics of the coherence can display more subtle changes with respect to the parameters of the quantum state. In the case of the XXZ Heisenberg model, the coherence changes from a monogamous to a polygamous nature. This allows us to define the shareability of coherence, leading to monogamy relations for coherence.

quant-ph↗

arXiv2013

Adiabatic thermostatistics of the two parameter entropy and the role of Lambert's W-function in its applications

A unified framework to describe the adiabatic class of ensembles in the generalized statistical mechanics based on Schwammle-Tsallis two parameter (q, q') entropy is proposed. The generalized form of the equipartition theorem, virial theorem and the adiabatic theorem are derived. Each member of the class of ensembles is illustrated using the classical nonrelativistic ideal gas and we observe that the heat functions could be written in terms of the Lambert's W-function in the large N limit. In the microcanonical ensemble we study the effect of gravitational field on classical nonrelativistic ideal gas and a system of hard rods in one dimension and compute their respective internal energy and specific heat. We found that the specific heat can take both positive and negative values depending on the range of the deformation parameters, unlike the case of one parameter Tsallis entropy.

cond-mat.stat-mech↗

arXiv2013

A Fractional entropy in Fractal phase space: properties and characterization

A two parameter generalization of Boltzmann-Gibbs-Shannon entropy based on natural logarithm is introduced. The generalization of the Shannon-Kinchinn axioms corresponding to the two parameter entropy is proposed and verified. We present the relative entropy, Jensen-Shannon divergence measure and check their properties. The Fisher information measure, relative Fisher information and the Jensen-Fisher information corresponding to this entropy are also derived. The canonical distribution maximizing this entropy is derived and is found to be in terms of the Lambert's W function. Also the Lesche stability and the thermodynamic stability conditions are verified. Finally we propose a generalization of a complexity measure and apply it to a two level system and a system obeying exponential distribution. The results are compared with the corresponding ones obtained using a similar measure based on the Shannon entropy.

cond-mat.stat-mech↗

arXiv2011

A class of energy based ensembles in Tsallis statistics

A comprehensive investigation is carried out on the class of energy based ensembles. The eight ensembles are divided into two main classes. In the isothermal class of ensembles the individual members are at the same temperature. A unified framework is evolved to describe the four isothermal ensembles. Such a description is provided both in the second and the third constraint formalisms. The isothermal- isobaric, grandcanonical and the generalized ensembles are illustrated through a study of the classical nonrelativistic and the extreme relativistic ideal gas models. In the adiabatic class of ensembles the individual members of the ensemble have the same value of the heat function and a unified formulation to described all the four ensembles is given. The nonrelativistic and the extreme relativistic ideal gases are studied in the isoenthalpic-isobaric ensemble, the adiabatic ensemble with number fluctuations, and, the adiabatic ensemble with number and particle fluctuations.

cond-mat.stat-mech↗

arXiv2010

Extended Curie-Weiss law: a nonextensive perspective

In the framework of the Tsallis nonextensive statistical mechanics we study an assembly of N spins, first in a background magnetic field, and then assuming them to interact via a long-range homogeneous mean field. To take into account the spin fluctuations the dynamical field coefficient is considered to be linearly dependent on the temperature. The physical quantities are evaluated using a perturbative expansion in the nonextensivity parameter (1-q). The extended Curie-Weiss law in the mean field case has been generalized. The critical temperature and the Curie- Weiss constant are found to be dependent on the nonextensivity parameter (1-q).

cond-mat.stat-mech↗

arXiv2009

Nonextensive statistics of relativistic ideal gas

We obtain the specific heat in the third constraint scenario for a canonical ensemble of a nonextensive extreme relativistic ideal gas in a closed form. The canonical ensemble of N particles in D dimensions is well-defined for the choice of the deformation parameter in the range 0 < q < 1 + 1 / DN. For a relativistic ideal gas with particles of arbitrary mass a perturbative scheme in the nonextensivity parameter (1 - q) is developed by employing an infinite product expansion of the q-exponential, and a direct transformation of the internal energy from the second to the third constraint picture. All thermodynamic quantities may be uniformly evaluated to any desired perturbative order.

cond-mat.stat-mech↗

arXiv2007

Rigid rotators and diatomic molecules via Tsallis statistics

We obtain an analytic expression for the specific heat of a system of N rigid rotators exactly in the high temperature limit, and via a pertubative approach in the low temperature limit. We then evaluate the specific heat of a diatomic gas with both translational and rotational degrees of freedom, and conclude that there is a mixing between the translational and rotational degrees of freedom in nonextensive statistics.

cond-mat.stat-mech↗